Find the scalar and vector components of `vec(a)` in the direction of `vec(b)` where
` vec(a) = hat (i) + hat(j) and vec(b) = hat (j) + hat (k) `

Find the scalar and vector components of vec(a) in the direction of vec(b) where vec(a) = 3 hat (i) + vec(j) + 3 hat (k) and vec(b) = hat (i) - hat (j) - hat (k)

Find the scalar and vector projection of vec(b) on a vec (a) where vec(a) = hat (i) + 2 hat (j) + 2 hat (k) and vec (b) = hat (j) + 2 hat (k)

Find a unit vector in the direction of (vec(a)+vec(b)) , where : vec(a)=2hat(i)+2hat(j)-5hat(k) and vec(b)=2hat(i)+hat(j)+3hat(k) .

Find the unit vector in the direction of vec(a)-vec(b) , where : vec(a)=hat(i)+3hat(j)-hat(k), vec(b)=3hat(i)+2hat(j)+hat(k) .

Find the projection of vector (vec(b)+vec (a )) on vector vec(a) where vec(a) = 2 hat (i) - hat (j) + 2 hat (k) and vec(b) = hat(j) + 2 hat (k)

Find vec(c) , when vec(a) xx vec(c) = vec(b) and vec(a).vec(c) =3 where vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(j) - hat(k)

Find the projection of vector (vec(b)+vec(c )) on vector vec(a) where vec(a) = hat (i) + 2 hat (j) + hat (k) , vec(b) = hat (i) + 3 hat (j) + hat (k) and vec c = hat (i) + hat (k)

Find a unit vector in direction of vec a-vec b , when vec a = 4 hat i + 7 hat j + hat k and vec b =3 hat j-11 hat k .

Find the (a) scalar component and (b) vector component of vec(A) = 3 hat(i) + 4 hat(j) + 5 hat(k) on vec(B) = hat(i) + hat(j) + hat(k) .